Discrete-Time Goldfishing
The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several o...
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| Видавець: | Інститут математики НАН України |
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| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147409 |
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| Цитувати: | Discrete-Time Goldfishing / F. Calogero // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1474092019-02-15T01:23:58Z Discrete-Time Goldfishing Calogero, F. The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems ''of goldfish type'' have been identified over time, featuring, in the right-hand (''forces'') side of their Newtonian equations of motion, in addition to other contributions, a velocity-dependent term such as that appearing in the right-hand side of the first formula mentioned above. The solvable character of these models allows detailed analyses of their behavior, which in some cases is quite remarkable (for instance isochronous or asymptotically isochronous). In this paper we introduce and discuss various discrete-time dynamical systems, which are as well solvable, which also display interesting behaviors (including isochrony and asymptotic isochrony) and which reduce to dynamical systems of goldfish type in the limit when the discrete-time independent variable l=0,1,2,... becomes the standard continuous-time independent variable t, 0≤t<∞. 2011 Article Discrete-Time Goldfishing / F. Calogero // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J35; 37C27; 70F10; 70H06 DOI: http://dx.doi.org/10.3842/SIGMA.2011.082 http://dspace.nbuv.gov.ua/handle/123456789/147409 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems ''of goldfish type'' have been identified over time, featuring, in the right-hand (''forces'') side of their Newtonian equations of motion, in addition to other contributions, a velocity-dependent term such as that appearing in the right-hand side of the first formula mentioned above. The solvable character of these models allows detailed analyses of their behavior, which in some cases is quite remarkable (for instance isochronous or asymptotically isochronous). In this paper we introduce and discuss various discrete-time dynamical systems, which are as well solvable, which also display interesting behaviors (including isochrony and asymptotic isochrony) and which reduce to dynamical systems of goldfish type in the limit when the discrete-time independent variable l=0,1,2,... becomes the standard continuous-time independent variable t, 0≤t<∞. |
| format |
Article |
| author |
Calogero, F. |
| spellingShingle |
Calogero, F. Discrete-Time Goldfishing Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Calogero, F. |
| author_sort |
Calogero, F. |
| title |
Discrete-Time Goldfishing |
| title_short |
Discrete-Time Goldfishing |
| title_full |
Discrete-Time Goldfishing |
| title_fullStr |
Discrete-Time Goldfishing |
| title_full_unstemmed |
Discrete-Time Goldfishing |
| title_sort |
discrete-time goldfishing |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147409 |
| citation_txt |
Discrete-Time Goldfishing / F. Calogero // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT calogerof discretetimegoldfishing |
| first_indexed |
2023-05-20T17:27:39Z |
| last_indexed |
2023-05-20T17:27:39Z |
| _version_ |
1796153340945498112 |